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<h1 id="tidesType">Tides</h1><p>
This class computes functionals of the time depending tide potential,
e.g potential, acceleration or gravity gradients.</p><p>If several instances of the class are given the results are summed up.
Before summation every single result is multiplicated by a <strong class="groops-config-element">factor</strong>.
To get the difference between two ocean tide models you must choose one factor by 1
and the other by -1. To get the mean of two models just set each factor to 0.5.
</p>

<h2 id="astronomicalTide">AstronomicalTide</h2><p>
This class computes the tide generating potential (TGP) of sun, moon
and planets (Mercury, Venus, Mars, Jupiter, Saturn).
It takes into account the flattening of the Earth (At the moment only at the acceleration level).</p><p>The computed result is multiplied with <strong class="groops-config-element">factor</strong>.
</p>
<table class="table table-hover">
<tr class="table-primary"><th>Name</th><th>Type</th><th>Annotation</th></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">useMoon</div></div></td><td>boolean</td><td>TGP of moon</td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">useSun</div></div></td><td>boolean</td><td>TGP of sun</td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">usePlanets</div></div></td><td>boolean</td><td>TGP of planets</td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">useEarth</div></div></td><td>boolean</td><td>TGP of Earth</td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">c20Earth</div></div></td><td>double</td><td>J2 flattening of the Earth</td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">factor</div></div></td><td>double</td><td>the result is multplied by this factor, set -1 to substract the field</td></tr>
</table>

<h2 id="earthTide">EarthTide</h2><p>
This class computes the earth tide according to the IERS2003 conventions.
The values of solid Earth tide external potential Love numbers and
the frequency dependent corrections of these values are given in the file
<a class="groops-class" href="fileFormat_earthTide.html">inputfileEarthtide</a>. The effect of the permanent tide is removed if
<strong class="groops-config-element">includePermanentTide</strong> is set to false.</p><p>The computed result is multiplied with <strong class="groops-config-element">factor</strong>.
</p>
<table class="table table-hover">
<tr class="table-primary"><th>Name</th><th>Type</th><th>Annotation</th></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config mustset">inputfileEarthtide</div></div></td><td>filename</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">includePermanentTide</div></div></td><td>boolean</td><td>results in FALSE: zero tide, TRUE: tide free gravity field</td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">factor</div></div></td><td>double</td><td>the result is multplied by this factor, set -1 to substract the field</td></tr>
</table>

<h2 id="poleTide">PoleTide</h2><p>
The potential coefficients of the solid Earth pole tide according to the
IERS2003 conventions are given by
\[
\begin{split}
\Delta c_{21} &= s\cdot(m_1 + o\cdot m_2), \\
\Delta s_{21} &= s\cdot(m_2 - o\cdot m_1),
\end{split}
\]with $s$ is the <strong class="groops-config-element">scale</strong>, $o$ is the <strong class="groops-config-element">outPhase</strong> and
$(m_1,m_2)$ are the wobble variables in seconds of arc.
They are related to the polar motion variables $(x_p,y_p)$ according to
\[
\begin{split}
m_1 &=  (x_p - \bar{x}_p), \\
m_2 &= -(y_p - \bar{y}_p),
\end{split}
\]The mean pole $(\bar{x}_p, \bar{y}_p)$ is approximated by a polynomial
read from <a class="groops-class" href="fileFormat_meanPolarMotion.html">inputfileMeanPole</a>.</p><p>The displacment is calculated with
\[
\begin{split}
S_r          &= -v\sin2\vartheta(m_1\cos\lambda+m_2\sin\lambda),\\
S_\vartheta &= -h\cos2\vartheta(m_1\cos\lambda+m_2\sin\lambda),\\
S_\lambda   &=  h\cos\vartheta(m_1\sin\lambda-m_2\cos\lambda),
\end{split}
\]where $h$ is the <strong class="groops-config-element">horizontalDisplacement</strong>
and $v$ is the <strong class="groops-config-element">verticalDisplacement</strong>.</p><p>The computed result is multiplied with <strong class="groops-config-element">factor</strong>.
</p>
<table class="table table-hover">
<tr class="table-primary"><th>Name</th><th>Type</th><th>Annotation</th></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">scale</div></div></td><td>double</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">outPhase</div></div></td><td>double</td><td></td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config mustset">inputfileMeanPole</div></div></td><td>filename</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">horizontalDisplacement</div></div></td><td>double</td><td>[m]</td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">verticalDisplacement</div></div></td><td>double</td><td>[m]</td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">factor</div></div></td><td>double</td><td>the result is multplied by this factor, set -1 to substract the field</td></tr>
</table>

<h2 id="oceanPoleTide">OceanPoleTide</h2><p>
The ocean pole tide is generated by the centrifugal effect of polar motion on the oceans.
The potential coefficients of this effect is given by
IERS2003 conventions are given by
\[
\begin{Bmatrix}
\Delta c_{nm}  \\
\Delta s_{nm}
\end{Bmatrix}=
\begin{Bmatrix}
c_{nm}^R  \\
s_{nm}^R
\end{Bmatrix}
(m_1\gamma^R+m_2\gamma^I)+
\begin{Bmatrix}
c_{nm}^I  \\
s_{nm}^I
\end{Bmatrix}
(m_2\gamma^R-m_1\gamma^I)
\]where the coefficients are read from file <a class="groops-class" href="fileFormat_oceanPoleTide.html">inputfileOceanPole</a>,
$\gamma=\gamma^R+i\gamma^I$ is given by <strong class="groops-config-element">gammaReal</strong> and
<strong class="groops-config-element">gammaImaginary</strong> and $(m_1,m_2)$ are the wobble variables in radians.
They are related to the polar motion variables $(x_p,y_p)$ according to
\[
\begin{split}
m_1 &=  (x_p - \bar{x}_p), \\
m_2 &= -(y_p - \bar{y}_p),
\end{split}
\]The mean pole $(\bar{x}_p, \bar{y}_p)$ is approximated by a polynomial
read from <a class="groops-class" href="fileFormat_meanPolarMotion.html">inputfileMeanPole</a>.</p><p>The computed result is multiplied with <strong class="groops-config-element">factor</strong>.
</p>
<table class="table table-hover">
<tr class="table-primary"><th>Name</th><th>Type</th><th>Annotation</th></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config mustset">inputfileOceanPole</div></div></td><td>filename</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">minDegree</div></div></td><td>uint</td><td></td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">maxDegree</div></div></td><td>uint</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">gammaReal</div></div></td><td>double</td><td></td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">gammaImaginary</div></div></td><td>double</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config mustset">inputfileMeanPole</div></div></td><td>filename</td><td></td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">factor</div></div></td><td>double</td><td>the result is multplied by this factor, set -1 to substract the field</td></tr>
</table>

<h2 id="doodsonHarmonicTide">DoodsonHarmonicTide</h2><p>
The time variable potential of ocean tides is given by a fourier expansion
\[
V(\M x,t) = \sum_{f} V_f^c(\M x)\cos(\Theta_f(t)) + V_f^s(\M x)\sin(\Theta_f(t)),
\]where $V_f^c(\M x)$ and $V_f^s(\M x)$ are spherical harmonics expansions and are
read from the file <a class="groops-class" href="fileFormat_doodsonHarmonic.html">inputfileDoodsonHarmonic</a>.
If set the expansion is limited in the range between <strong class="groops-config-element">minDegree</strong>
and <strong class="groops-config-element">maxDegree</strong> inclusivly.
$\Theta_f(t)$ are the arguments of the tide constituents $f$:
\[
\Theta_f(t) = \sum_{i=1}^6 n_f^i\beta_i(t),
\]where $\beta_i(t)$ are the Doodson's fundamental arguments ($\tau,s,h,p,N',p_s$)
and $n_f^i$ are the Doodson multipliers for the term at frequency $f$.</p><p>The major constituents given by <a class="groops-class" href="fileFormat_doodsonHarmonic.html">inputfileDoodsonHarmonic</a> can be used to
interpolate minor tidal constituents using the file <a class="groops-class" href="fileFormat_admittance.html">inputfileAdmittance</a>.
This file can be created with <a class="groops-program" href="DoodsonHarmonicsCalculateAdmittance.html">DoodsonHarmonicsCalculateAdmittance</a>.</p><p>After the interpolation step a selection of the computed constituents can be
choosen by <a class="groops-class" href="doodson.html">selectDoodson</a>. Only these constiuents are considered for the results.
If no <a class="groops-class" href="doodson.html">selectDoodson</a> is set all constituents will be used. The constituents can
be coded as Doodson number (e.g. 255.555) or as names intoduced by Darwin (e.g. M2).</p><p>The computed result is multiplied with <strong class="groops-config-element">factor</strong>.
</p>
<table class="table table-hover">
<tr class="table-primary"><th>Name</th><th>Type</th><th>Annotation</th></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config mustset">inputfileTides</div></div></td><td>filename</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">inputfileAdmittance</div></div></td><td>filename</td><td>interpolation of minor constituents</td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional-unbounded">selectDoodson</div></div></td><td><a href="doodson.html">doodson</a></td><td>consider only these constituents, code number (e.g. 255.555) or darwin name (e.g. M2)</td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">minDegree</div></div></td><td>uint</td><td></td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">maxDegree</div></div></td><td>uint</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">nodeCorr</div></div></td><td>uint</td><td>nodal corrections: 0-no corr, 1-IHO, 2-Schureman</td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">factor</div></div></td><td>double</td><td>the result is multplied by this factor, set -1 to substract the field</td></tr>
</table>

<h2 id="centrifugal">Centrifugal</h2><p>
Computes the centrifugal potential in a rotating system
\[
V(\M r, t) = \frac{1}{2} (\M\omega(t)\times\M r)^2.
\]The current rotation vector $\M\omega(t)$ is computed from the
<a class="groops-class" href="earthRotationType.html">earthRotation</a>
provided by the calling program.
The computed result is multiplied with <strong class="groops-config-element">factor</strong>.</p><p>Be careful, the centrifugal potential is not harmonic.
Convolution with a harmonic kernel (e.g. to compute gravity
anomalies) is not meaningful.
</p>
<table class="table table-hover">
<tr class="table-primary"><th>Name</th><th>Type</th><th>Annotation</th></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">factor</div></div></td><td>double</td><td>the result is multplied by this factor, set -1 to substract the field</td></tr>
</table>

<h2>SolidMoonTide</h2><p>
This class computes the solid moon tide according to the IERS2010 conventions.
The values of solid Moon tide external potential Love numbers are given and
there are no frequency dependent corrections of these values.
The computed result is multiplied with <strong class="groops-config-element">factor</strong>.
</p>
<table class="table table-hover">
<tr class="table-primary"><th>Name</th><th>Type</th><th>Annotation</th></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">k20</div></div></td><td>double</td><td></td></tr>
<tr class=""><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">k30</div></div></td><td>double</td><td></td></tr>
<tr class="table-light"><td class="m-0"><div class="h-100 config-tree depth-0"><div class="h-100 config optional">factor</div></div></td><td>double</td><td>the result is multplied by this factor, set -1 to substract the field</td></tr>
</table>

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